Preheat an oven to 325°F. In a Dutch oven over medium-high heat, warm 2 Tbs. of the olive oil. Season the short ribs with 2 tsp. of the salt and the pepper. Working in batches, add the short ribs to the pot and cook, turning occasionally, until browned on all sides, 5 to 6 minutes per batch. Transfer to a plate.
In the same pot over medium-high heat, warm the remaining 1 Tbs. olive oil. Add the onion and carrots and cook, stirring occasionally, until the onion softens, about 5 minutes. Stir in the garlic and cook until fragrant, about 1 minute. Sprinkle in the flour and stir well. Slowly stir in the wine, then the stock. Stir in the tomato paste, rosemary and bay leaf. Return the short ribs to the pot. They should be barely covered with liquid; if not, add hot water as needed. Bring the liquid to a boil, cover the pot and transfer to the oven. Cook, moving the position of the ribs every 45 minutes or so to be sure they are covered with liquid, until very tender, about 2 1/2 hours. Transfer the ribs to a deep platter (it’s OK if the meat separates from the bones) and cover loosely with aluminum foil.
Let the cooking liquid stand for 5 minutes, then skim off the fat. Bring the liquid to a boil over high heat and cook, stirring, until reduced by one-fourth, about 10 minutes. Discard the bay leaf. Return the short ribs to the pot.
Just before serving, make the polenta: In a heavy saucepan over high heat, bring 3 cups water, the milk and the remaining 2 tsp. salt to a boil. Slowly whisk in the polenta, then reduce the heat to medium-low. Cook, whisking often, until the polenta is thick, about 2 minutes. Stir in the 1/2 cup cheese. Divide the polenta among warmed deep bowls, and top with the ribs and sauce. Serve immediately and pass additional cheese alongside.
Adapted from Williams-Sonoma Comfort Food, by Rick Rodgers (Oxmoor House, 2009).